Question

The points A(–5, 5) and B(–5, –7) are plotted on the coordinate plane.

Graph where both the axes run from minus six to plus six and beyond. Straight line AB intersect the x- axis at (-5, 0). The coordinates are A(-5, 5) and B(-5, -7)

On paper, make a rectangle that has points A and B as two of its vertices and has a perimeter of 40 units. Draw and label the two other vertices as points C and D on the coordinate plane. Draw line segments to show the rectangle.
What are the coordinates for points C and D? Select all that apply.
A. (–5, 5)
B. (3, 5)
C. (11, 5)
D. (3, –7)
E. (11, 7)
F. (11, –7)

Answer 1

C I did this before

Answer 2

Given points A(-5, 5) and B(-5, -7), and a rectangle's perimeter of 40 units, we calculate the width of the rectangle to be 8 units. Thus, the coordinates for points C and D will be C(3, 5) and D(3, -7).

Step-by-step explanation:

Given points A(-5, 5) and B(-5, -7), these will form the vertical sides of the rectangle since they have the same x-coordinates. To find points C and D, we need to calculate the length of the sides of the rectangle based on the given perimeter of 40 units. The vertical side length is the difference in y-coordinates of B and A, i.e. |-7 - (-5)| = 12 units. A rectangle's perimeter is calculated as 2*(length + width), thus the width of the rectangle would be (40 - 2*12)/2 = 8 units.

Therefore, the x-coordinates of points C and D will be -5 + 8 = 3 units, and as a result, points C and D will have coordinates C(3, 5) and D(3, -7), respectively. This gives us options B and D as the correct choices.

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